Originally Posted by
Middle_Seat
Nara and Himeji look like good options near Kyoto. Are there similar day trip options near Tokyo?
Yes - Kamakura, Nikko, Hakone come to mind. I recommend getting a guide book.
Originally Posted by
Middle_Seat
Would it be reasonable, on the train ride from Tokyo to Kyoto, to do a brief stopover near Mt. Fuji?
Not really. If you take a fast train on the main Shinkansen line to Kyoto, you won't stop anywhere near Fuji. If you take a slower train that stops at the smaller cities you could get off at Shin Fuji station but it's not a great place for a walk:
https://www.google.co.uk/maps/@35.14...7i13312!8i6656